Top Banner

of 14

MAT135_TT2_2009F.pdf

Jun 03, 2018

Download

Documents

examkiller
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript

  • 8/12/2019 MAT135_TT2_2009F.pdf

    1/14

    Code:9146DEPARTMENT OF MATHEMATICSUniversity of Toronto

    MAT 135YTerm Test ff2Thursday December 3, 2009Time allowed: t hour, 45 minutes

    PLEASEPRINT n INK oTBALLPOINT PEN:NAME OF STUDENT:(Please RINT full nameandUNDERLINEsurname):STUDENT NUMBER:SIGNATURE OF STUDENT(in INK or BALLPOINT PEN):TUTORIAL CODE (e.g.M4A,RbD,etc.):TUTORIAT TIME (r.S.T4, R6,F3,etc.):NAME OF YOUR T.A.:

    NOTE:1. Beforeyou start, check hat this test has 14 pages.

    There are NO blank pages.2. This test consistsof 20 multiple-choicequestions.

    rndicate your answer to each question by completelyfilling in the appropriate circle in the ANSWER Boxon this front pege. (Use a sharp dark pencil ) -3. No aids allowed. No calculators

    ANSWERBOX1 . @ @ @ O @2 . @ @ @ @ @3 . @ @ @ @ @4 . @ ) @ @ @5 . @ @ @ O @6 . @ @ @ @ @7 . @ @ @ @ @8 . @ @ @ O @e . @ @ @ o

    1 0 . @ @ @ @1 1 . @ @ @ @1 2 . @ @ @ O @1 3 . @ @ @ @1 4 . @ @ @ O @1 5 . @ @ @ @ @1 6 . @ @ @ @ @1 7 . @ @ @ O @1 8 . @ @ @ O @l e . @ @ @ o @2 0 . @ @ @ @ @

    PageL of L4

  • 8/12/2019 MAT135_TT2_2009F.pdf

    2/14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    3/14

    DI TEPenalty forperpendicular to thecurve( -24,0)(52, )(0 ,0)(32,0)(24,0)

    s minus 10 marksat the point (2,b) will intersect

    Code: 914the r-axis at the

    Ss o r+ 1.

    not doing

    U : t r 3 2 rhe linepoint@o@@@

    4. I f f ( r ) : no"rc tant r l@ :o@ :o@ t no *@ *

    then "(2) :

    Page3 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    4/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks5. If /(3) - -3, / '(3) - 5 ands@) - (2r2- s)/("), theng,(S)

    @ 2 4( D 1 4@ -r2o - B@ 2 0

    Code:914

    6. If 2r2* rA * As 6r + 14,o - *@ ;@ *@ - :o@ #

    f ind the value ' d', t d* at the point where tr :3, A : 2.

    Page4 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    5/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks Code: 9147. Supposehat a ball is thrown upward n sucha way hat its heightabove he grounda.fter secondsnflight is (6+ 32t t1t2) feet.What is the maximum eightattainedby the ball?

    @ 32 feeiQ 22 leet@ 18 eet@ 30 feet@ 26feet

    8' Eachside of a squa.res increasingat 3 ft/sec. At the moment when the area of the squa"res 25 sq ft,how fast is the area increasing?@ 32 sq ft/secQ 30 sq ft/sec@ 36 sq ft/sec@ 26 sq ft/sec@ 28 sq ft/sec

    Page5 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    6/14

    Y N THE FRONT PAGPenalty for not doing so is minus 10 markse. Let f (r) -MeanValue@ i

    @ ;e io :

    3@ ,

    4r2 3r on U,41. Find theTheorem. number c between 1 and 4 that satisfiesCode: 91

    the conclusion f th

    10.Thegraphof U 2r3 Br2@ 4@ 2@ oo - 3@ - 5

    - 72r hasa localmaximumat r :

    Page6 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    7/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks11. The graph of U - tre2*has a point of inflection at r -

    G ) 4o - 1G ) - 3@ ) - 4@ 2

    L2. The graph of U : 14 * 2rs - 3612* br - 4 is concavedown on the interval@ (-3 ,2 )@ (-4,1)@ (3 ,5 )@ (-5, -2)@ (0,3)

    Code: 9146

    Page7 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    8/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGE. Penalty for not doing so is minus 10 marks Code:9146zx3+x2 - i,2x 6 -rJ. rne grapnoI A : dx +S\ has wo verticalasymptotesnd alsohas oneslant (i.e. obliqueasymptote, hich s the iire

    @ u : 2 c + 2@a : z ' - +@ a : 2 r + l@ v : 2 ,O a : 2 x - 5

    14. The sumof twopositivenumberss 8. What s thesma,llestossible alueof the sumof theirsquares?@ 3 4o 3 2@ 3 6o 3 0@ 2 8

    PageB of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    9/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks15. Let f (r) - - -. Then / hase r - r

    @ two horizontal asymptotes and one vertical asympotote@ one hori zontal asymptote and no vertical asympototes@ one hori zontal asymptote and one vertical asympotote@ oo horizontal asymptotes and no vertical asympototesQ two horizontal asymptotes and no vertical as.ympototes

    Code: 9146

    Page9 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    10/14

    16.

    DICATE UR ANSWERS ON ONT PPenalty for not doing so is minus 10 marks Code: 914a r 4 + b r u + I(r - 1)sin(nr) (wherea and b areconstants) xistsanci s a finite number, ind its valuGiven hat limr-+7

    erJ@ 4t l6

    e t l,@ tt l 4I frt l@ not determinable du e to insufficient information abou a and,b

    Page10 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    11/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks Code: 9146^E17. There are exactly two points on the curve x:2/3 A2/3: 9 where he tangent line has slope9. Fiod th"slopeof the line joining those two points. - zq\/5rr9_5

    ,r- -L V a(B) - -V O| . g , - ,> / ;o - " I "- EJ,/Et F t _ _ 8

    Page11 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    12/14

    INDICATB YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks18. Let f (r) : r r ' , i .e. , to the power r* . F ind f , (2).

    e 32+ 64 n 2 + 64(tn2)2@ 32+32 lnz + }AQnz )2@ 32+ 321n2+ r2S(tn2)2@ 32 + 321n2+ 64(In2)2@ 32 + 64 n 2 + r2B(In2)2

    Code: 9146

    Page12 of 14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    13/14

  • 8/12/2019 MAT135_TT2_2009F.pdf

    14/14

    INDICATE YOUR ANSWERS ON THE FRONT PAGEPenalty for not doing so is minus 10 marks Code: 9L4620. There s onestraight line which is tangent to the ctrve 49 : z2 at a point ,4 and at the same ime tangentto the curve t:2A2 at,a point B. Find the distancebetween he points A and,B.

    ^ t ;e ?^ 5r/,@ "^ 5,/5rsr ,^ 3'/6( D ) - 2^ 8,/ze ,